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Power-law scaling and fractal nature of medium-range order in metallic glasses

Nature Materials volume 8, pages 30–34 (2009)Cite this article

Abstract

The atomic structure of metallic glasses has been a long-standing scientific problem. Unlike crystalline metals, where long-range ordering is established by periodic stacking of fundamental building blocks known as unit cells, a metallic glass has no long-range translational or orientational order, although some degrees of short- and medium-range order do exist1,2,3. Previous studies1,2,3,4 have identified solute- (minority atom)-centred clusters as the fundamental building blocks or short-range order in metallic glasses. Idealized cluster packing schemes, such as efficient cluster packing on a cubic lattice1 and icosahedral packing3 as in a quasicrystal, have been proposed and provided first insights on the medium-range order in metallic glasses. However, these packing schemes break down beyond a length scale of a few clusters. Here, on the basis of neutron and X-ray diffraction experiments, we propose a new packing scheme—self-similar packing of atomic clusters. We show that the medium-range order has the characteristics of a fractal network with a dimension of 2.31, and is described by a power-law correlation function over the medium-range length scale. Our finding provides a new perspective of order in disordered materials and has broad implications for understanding their structure–property relationship, particularly those involving a change in length scales.

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Figure 1: Power-law scaling of the FSDP (q1) versus atomic volume (va) for a variety of metallic glasses.
Figure 2: Correlation between FSDP and MRO.
Figure 3: Demonstration of fractal packing with experimental [g(r)−1].

References

  1. Miracle, D. B. A structural model for metallic glasses. Nature Mater. 3, 697–702 (2004).

    Article  CAS  Google Scholar 

  2. Miracle, D. B. The efficient cluster packing model—an atomic structural model for metallic glasses. Acta Mater. 54, 4317–4336 (2006).

    Article  CAS  Google Scholar 

  3. Sheng, H. W. et al. Atomic packing and short-to-medium-range order in metallic glasses. Nature 439, 419–425 (2006).

    Article  CAS  Google Scholar 

  4. Ma, D. et al. Nearest-neighbor coordination and chemical ordering in multicomponent bulk metallic glasses. Appl. Phys. Lett. 90, 211908 (2007).

    Article  Google Scholar 

  5. Manderlbrot, B. B. The Fractal Geometry of Nature (W. H. Freeman, 1983).

    Google Scholar 

  6. Gouyet, J.-F. Physics and Fractal Structures (Springer, 1996).

    Google Scholar 

  7. Freltoft, T., Kjems, J. K. & Sinha, S. K. Power-law correlations and finite-size effects in silica particle aggregates studied by small-angle neutron scattering. Phys. Rev. B 33, 269–275 (1986).

    Article  CAS  Google Scholar 

  8. Weitz, D. A., Huang, J. S., Lin, M. Y. & Sung, J. Dynamics of diffusion-limited kinetic aggregation. Phys. Rev. Lett. 53, 1657–1660 (1984).

    Article  CAS  Google Scholar 

  9. Feder, J., Jossang, T. & Rosenqvist, E. Scaling behaviour and cluster fractal dimension determined by light-scattering from aggregating proteins. Phys. Rev. Lett. 53, 1403–1406 (1984).

    Article  CAS  Google Scholar 

  10. Elliott, S. R. Physics of Amorphous Materials (Longman, 1984).

    Google Scholar 

  11. Borjesson, L., McGreevy, R. L. & Howells, W. S. Fractal aspects of superionic glasses from reverse Monte-Carlo simulations. Phil. Mag. B 65, 261–271 (1992).

    Article  Google Scholar 

  12. Fontana, A. et al. Low-frequency dynamics in superionic borate glasses by coupled Raman and inelastic neutron scattering. Phys. Rev. B 41, 3778–3785 (1990).

    Article  CAS  Google Scholar 

  13. Cullity, B. D. & Stock, S. R. Elements of X-Ray Diffraction (Prentice Hall, 2001).

    Google Scholar 

  14. Wang, X. L. The application of neutron diffraction to engineering problems. JOM 58, 52–57 (2006).

    Article  CAS  Google Scholar 

  15. Guinier, A. X-Ray Diffraction: in Crystals, Imperfect Crystals, and Amorphous Bodies (Dover, 1994).

    Google Scholar 

  16. Elliott, S. R. Medium-range structural order in covalent amorphous solids. Nature 354, 445–452 (1991).

    Article  CAS  Google Scholar 

  17. Mattern, N. et al. Short-range order of Zr62−xTixAl10Cu20Ni8 bulk metallic glasses. Acta Mater. 50, 305–314 (2002).

    Article  CAS  Google Scholar 

  18. Altounian, Z. & Stromolsen, J. O. Superconductivity and spin fluctuations in Cu–Zr, Ni–Zr, Co–Zr and Fe–Zr metallic glasses. Phys. Rev. B 27, 4149–4156 (1983).

    Article  CAS  Google Scholar 

  19. Buschow, K. H. J. Short-range order and thermal-stability in amorphous-alloys. J. Phys. F 14, 593–607 (1984).

    Article  CAS  Google Scholar 

  20. Calvayrac, Y. et al. On the stability and structure of Cu–Zr based glasses. Phil. Mag. B 48, 323–332 (1983).

    Article  CAS  Google Scholar 

  21. Price, D. L. et al. Intermediate-range order in glasses and liquids. J. Phys. C 21, L1069–L1072 (1988).

    Article  Google Scholar 

  22. Jiang, Q. K. et al. La-based bulk metallic glasses with critical diameter up to 30 mm. Acta Mater. 55, 4409–4418 (2007).

    Article  CAS  Google Scholar 

  23. Xi, X. K., Zhao, D. Q., Pan, M. X. & Wang, W. H. Highly processable Mg65Cu25Tb10 bulk metallic glass. J. Non-Cryst. Solids 344, 189–192 (2004).

    Article  CAS  Google Scholar 

  24. Li, S. et al. Formation and properties of RE55Al25Co20 (RE=Y, Ce, La, Pr, Nd, Gd, Tb, Dy, Ho and Er) bulk metallic glasses. J. Non-Cryst. Solids 354, 1080–1088 (2008).

    Article  CAS  Google Scholar 

  25. Mancini, L. et al. Hierarchical porosity in real quasicrystals. Phil. Mag. Lett. 78, 159–167 (1998).

    Article  CAS  Google Scholar 

  26. Janot, C. & Deboissieu, M. Quasi-crystals as a hierarchy of clusters. Phys. Rev. Lett. 72, 1674–1677 (1994).

    Article  CAS  Google Scholar 

  27. Takakura, H. et al. Atomic structure of the binary icosahedral Yb–Cd quasicrystal. Nature Mater. 6, 58–63 (2007).

    Article  CAS  Google Scholar 

  28. Sachdev, S. & Nelson, D. R. Order in metallic glasses and icosahedral crystals. Phys. Rev. B 32, 4592–4606 (1985).

    Article  CAS  Google Scholar 

  29. Sheng, H. W., Ma, E., Liu, H. Z. & Wen, J. Pressure tunes atomic packing in metallic glass. Appl. Phys. Lett. 88, 171906 (2006).

    Article  Google Scholar 

  30. Cargill, G. S. III. in Solid State Physics Vol. 30 (eds Feitz, F., Turnbull, D. & Ehrenreich, H.) 227–320 (Academic, 1975).

    Google Scholar 

  31. Manoharan, V. N. & Pine, D. J. Building materials by packing spheres. MRS Bull. 29, 91–95 (2004).

    CAS  Google Scholar 

  32. Nugent, C. R., Edmond, K. V., Patel, H. N. & Weeks, E. R. Colloidal glass transition observed in confinement. Phys. Rev. Lett. 99, 025702 (2007).

    Article  Google Scholar 

  33. Schall, P., Weitz, D. A. & Spaepen, F. Structural rearrangements that govern flow in colloidal glasses. Science 318, 1895–1899 (2007).

    Article  CAS  Google Scholar 

  34. Greer, A. L. & Ma, E. Bulk metallic glasses: At the cutting edge of metals research. MRS Bull. 32, 611–615 (2007).

    Article  CAS  Google Scholar 

  35. Yang, B., Liu, C. T. & Nieh, T. G. Unified equation for the strength of bulk metallic glasses. Appl. Phys. Lett. 88, 221911 (2006).

    Article  Google Scholar 

  36. Sietsma, J. & Thijsse, B. J. An investigation of universal medium range order in metallic glasses. J. Non-Cryst. Solids 135, 146–154 (1991).

    Article  CAS  Google Scholar 

  37. Orbach, R. Dynamics of fractal networks. Science 231, 814–819 (1986).

    Article  CAS  Google Scholar 

  38. Poulsen, H. F. et al. Measuring strain distributions in amorphous materials. Nature Mater. 4, 33–36 (2005).

    Article  CAS  Google Scholar 

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Acknowledgements

We thank Z. P. Lu and M. J. Kramer for providing the metallic-glass samples, H. Bei for help in density measurements and S. E. Nagler for helpful discussions. This research was supported by US Department of Energy, Office of Basic Energy Sciences, under Contract DE-AC05-00OR22725 with UT-Battelle, LLC.

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  1. Neutron Scattering Science Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA

    D. Ma, A. D. Stoica & X.-L. Wang

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  1. D. Ma
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  3. X.-L. Wang
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Correspondence to X.-L. Wang.

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Ma, D., Stoica, A. & Wang, XL. Power-law scaling and fractal nature of medium-range order in metallic glasses. Nature Mater 8, 30–34 (2009). https://doi.org/10.1038/nmat2340

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